"The 21 Million BTC limit

One somewhat controversial property of Bitcoin is its fixed currency supply. There are currently 25 BTC being generated every 10 minutes, and this amount cuts in half every four years. All in all, there will never be more than 21 million BTC in existence. On the other hand, each bitcoin can be split into 100 million pieces (called "satoshis"), so it will not become difficult to use Bitcoin if its value goes up the same way it would become problematic to trade with dollars if each penny was enough to buy a car. Thus, all in all, the total number of currency units that will ever exist stands at 2,100,000,000,000,000: 2.1 quadrillion, or about 250.899. In choosing this figure, Satoshi was much luckier, or wiser, than most people realize. First of all, the number is considerably less than 264 - 1, the largest integer that can be stored in a standard integer on a computer - go above that, and the integers wrap around to zero like an odometer.

Second, however, there is another, lower threshold that the total satoshi count manages to fall just below: the largest possible integer that can be exactly represented in floating point format. Integers are not the only kind of number that computers can store; to handle decimal numbers, computers use a format known as floating point representation. Floating point representation is essentially a binary version of scientific notation. For example, here are some values that you may be familiar with if you studied any physics:

    Mass of the Earth: 5.972 * 1024 kg
    Mass of the Sun: 1.989 * 1030 kg
    Speed of light: 2.998 * 108 m/s
    One lightyear: 9.460 * 1015 m
    Mass of a proton: 1.672 * 10-27 kg
    Planck length: 1.616 * 10-35 m

Notice how scientific notation allows you to express all of these values with reasonable accuracy despite their wildly varying scales. Floating point notation is essentially scientific notation in binary; when you store the number 9.625, your computer stores "1.001101 * 1011" (or rather, it stores 01000000 00100011 01000000 00000000 00000000 00000000 00000000 00000000, which is the same thing in high-precision serialized form). In this high-precision form, the "significand" (the part that's not the exponent) has 52 bits. What this means is that high-precision (more precisely, "double precision") floating point numbers are good enough to exactly store integers up to 253, but not higher - if you go higher, you start lopping off digits at the end. Bitcoin's 250.9 satoshis are, in exponential terms, just below this maximum. "